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The operator amenability of \(A(G)\). (English) Zbl 0842.43004
Let \(G\) be a locally compact group and \(A(G)\) its Fourier algebra. The main results in this paper are: (1) \(A(G)\) is operator amenable for every compact group \(G\); (2) the group \(G\) is amenable if and only if \(A(G)\) is operator amenable; (3) the \(C^*\)-algebra \(A\) is Banach algebra amenable if and only if \(A\) is operator amenable.

MSC:
43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
22D15 Group algebras of locally compact groups
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